If A abd Bare two sets, under what conditionsare A' and B' disjoint sets?
If A and B are independant sets, under what conditions are A' and B' are independant?
Let $\displaystyle C$ be the larger set where these two are contained in.
Now if $\displaystyle A\cup B \not = C$ then $\displaystyle \emptyset \not = (A\cup B)' = A' \cap B' $.
Thus, if we want $\displaystyle A' \cap B' = \emptyset$ it means $\displaystyle A\cup B = C$.